Time-frequency analysis has been used for detection and classification of features in electromagnetic (EM) data by generating time-frequency surfaces. Most techniques that exist for generating such surfaces assume a constantly-spaced sample structure. Further, most existing methods (e.g., Wigner-Ville, Short Time Fourier Transform STFT) employ batch mode processing, which results in some latency in real-time processing.
There is current interest in techniques that enable high-bandwidth data acquisition with limited sampling capability. This has led to exploration of nonconstant sampling and compressed sensing techniques for collecting relevant data structures. Many of the extant time-frequency analysis tools (e.g., MATLAB) will require a conversion of such data to conventional Nyquist sampling. Generally the problem is approached by using analog to digital (A/D) and analysis hardware that will support the necessary sample rates. Optimization of algorithms that perform constantly-spaced time-frequency analysis (e.g., fast fourier transform of the west “FFTW”) allows for the handling of greater amounts of data. These approaches generally require high sampling rates and do not address the case where Nyquist sampling is not possible.
A wide variety of signals and related protocols exist for the use of radio frequency (RF) signals in communication systems and other devices, such as radar systems. In some applications, it is desirable to determine or confirm the existence of RF signals and accurately measure their parameters. RF signals of interest, however, can occur across a wide range of center frequencies with various bandwidths and can be relatively small in amplitude compared to background noise. As such, it is desirable for an RF receiver to be designed to acquire and allow the detection and measurement of signals across a wide frequency range with various bandwidths while contributing little distortion, spurs or interference from its own circuitry. For a electronic intelligence application, for example, the desired signals to be acquired and detected can fall within a frequency range from less than 2 GHz to greater then 20 GHz. To provide reasonable sensitivity against a variety of signal types and bandwidths while maximizing search coverage, typical instantaneous search bandwidths may range from 100 MHz or less to 1 GHz or greater.
Many receiver architectures currently exist for receiving and detecting RF signals. These architectures include heterodyne receivers, homodyne receivers (also called zero-IF and direct conversion receivers for intermediate frequency (IF) applications), low-IF receivers, double conversion wideband IF receivers, wideband digital receivers, 6-port receivers (a special case of homodyne receivers), 3-phase variations of homodyne receivers, charge-domain direct RF mixer-sampler receivers, compressive receivers, noise-shaping sigma-delta receivers, non-reconfigurable direct RF optical down-sampling receivers, bandpass sampling variations of heterodyne receivers, and optical tuned channelized filters for fiberoptic WDM (wavelength division multiplexed) receivers. In addition, multi-signal bandpass sampling receivers combining the outputs from multiple bandpass filters without tuning have been proposed. In addition, noise-shaping sigma delta converters that use a bank of bandpass filters to implement a tuning function with a modulation sampling clock meeting the Nyquist criteria for the total frequency range of interest have been designed. In addition, direct RF receivers based on the use of analog high-speed pre-samplers have been built, although not in any reconfigurable architecture. Still further, combination architectures have been utilized such as a combination of switched homodyne receiver and low-IF receiver architectures.
For wideband applications, sampling at the Nyquist rate of at least twice the bandwidth can be very difficult because of device limitations, power consumption, size, weight, and cost. In order to avoid these difficulties, sub-Nyquist sampling schemes have been proposed including various non-uniform sampling techniques for harmonic retrieval and some recent methods in compressive sensing (also referred to as compressive sampling). Non-uniform sampling techniques proposed to date have, however, been limited in the types of signals that can be processed (generally extremely narrow-band signals), number of simultaneous signals (one or two typically), and total decimation ratio (typically ⅕ to 1/10 Nyquist at best). Compressive sensing techniques suffer from numerous challenges, including device implementation, computational complexity in their reconstruction modules, and signal reconstruction.
Each of these prior architectures suffer certain disadvantages and, therefore, have not been entirely effective in receiving and detecting RF signals, particularly in applications requiring reconfigurability for variable signal environment; the ability to reconstruct the signal; reasonable sensitivity; low size, weight, cost, and power; large frequency range of interest that may span many GHz; including applications such as radar warning receivers, electronic support receivers, electronic support measures receivers, electronic intelligence, communications intelligence, and ultra wideband radar receiver applications.